This invention relates to a novel combinatorial device which provides increased educational opportunities in the study of combinatorics, as well as a pastime novelty device for those simply seeking a more mentally challenging novelty. Specifically, the present invention is to a twenty-sided regular polyhedron known as an icosahedron.
Regular polyhedra are uniform (all of its vertices are the same or congruent) and have faces of all of one kind of congruent regular polygon. There are five regular polyhedra. The regular polyhedra were an important part of Plato's natural philosophy, and thus have come to be called the Platonic Solids. These five regular polyhedra are the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron.
A semiregular polyhedron has regular polygons as faces, but the faces are not of the same kind. As in regular polyhedra, the vertices are congruent. There are thirteen semiregular polyhedra. It is generally believed that they were described by Archimedes, and thus are called the Archimedean Polyhedra.
The "Magic Cube", also known as "Rubik's Cube", has offered the mathematics, architectural, computer, and puzzle world with the most imaginative and challenging combinatorial device since Sam Loyd's famous 14/15 Puzzle which came out in the 19th century. Structurally, the "Magic Cube" is formed by three types of cube members: six center cubes, twelve edge cubes, and eight corner cubes. The center cubes have only one face portion which is involved in the numerous orientations possible in the device. However, the edge cubes have two such face portions, and the corner cubes have three such face portions. The six center cubes are attached to axles which issue from a central spindle. Each of the other cube members has small projections or ledges which interlock with other cube members; the center cubes act as keystones.
Following the initial commercial success of the "Magic Cube," a number of variations of this basic device were developed. Structurally, these variations were nearly identical to that described above. By retaining the same structural construction, assurance that the device would operate was provided. To achieve one of the variations, for example, the edges of the "Magic Cube" were cut off, yielding a truncated cube now having a total of fourteen faces rather than the six faces of an original cube. In the original "Magic Cube" the six faces were each square; in the truncated cube, there are eight triangular faces and six octagonal faces. Thus, the truncated cube is a semiregular polyhedron. In the original cube there were eight vertices, each with three edges meeting; in the truncated cube there are twentyfour vertices, each having three edges meeting. Other variations to the "Magic Cube" include removing all edges and forming a sphere, or rounding four sides and forming a cylinder.